17 Language support library [support] (original) (raw)

17.12 Comparisons [cmp]

17.12.4 Concept three_way_comparable [cmp.concept]

Let t and u be lvalues of types const remove_reference_t<T> andconst remove_reference_t, respectively.

T and U modelpartially-ordered-with<T, U> only if

t < u,t <= u,t > u,t >= u,u < t,u <= t,u > t, andu >= t have the same domain,
bool(t < u) == bool(u > t) is true,
bool(u < t) == bool(t > u) is true,
bool(t <= u) == bool(u >= t) is true, and
bool(u <= t) == bool(t >= u) is true.

template<class T, class Cat = partial_ordering> concept three_way_comparable = weakly-equality-comparable-with<T, T> && partially-ordered-with<T, T> && requires(const remove_reference_t<T>& a, const remove_reference_t<T>& b) { { a <=> b } -> compares-as<Cat>;};

Let a and b be lvalues of type const remove_reference_t<T>.

T and Catmodel three_way_comparable<T, Cat> only if

(a <=> b == 0) == bool(a == b) is true,
(a <=> b != 0) == bool(a != b) is true,
((a <=> b) <=> 0) and (0 <=> (b <=> a)) are equal,
(a <=> b < 0) == bool(a < b) is true,
(a <=> b > 0) == bool(a > b) is true,
(a <=> b <= 0) == bool(a <= b) is true,
(a <=> b >= 0) == bool(a >= b) is true, and
if Cat is convertible to strong_ordering, T modelstotally_ordered ([concept.totallyordered]).

template<class T, class U, class Cat = partial_ordering> concept three_way_comparable_with = three_way_comparable<T, Cat> && three_way_comparable<U, Cat> && comparison-common-type-with<T, U> && three_way_comparable< common_reference_t<const remove_reference_t<T>&, const remove_reference_t&>, Cat> && weakly-equality-comparable-with<T, U> && partially-ordered-with<T, U> && requires(const remove_reference_t<T>& t, const remove_reference_t& u) { { t <=> u } -> compares-as<Cat>;{ u <=> t } -> compares-as<Cat>;};

Let t and t2 be lvalues denoting distinct equal objects of types const remove_reference_t<T> andremove_cvref_t<T>, respectively, and let u and u2 be lvalues denoting distinct equal objects of types const remove_reference_t andremove_cvref_t, respectively.

Let C becommon_reference_t<const remove_reference_t<T>&, const remove_reference_t&>.

T, U, and Catmodel three_way_comparable_with<T, U, Cat> only if

t <=> u and u <=> t have the same domain,
((t <=> u) <=> 0) and (0 <=> (u <=> t)) are equal,
(t <=> u == 0) == bool(t == u) is true,
(t <=> u != 0) == bool(t != u) is true,
Cat(t <=> u) == Cat(CONVERT_TO_LVALUE<C>(t2) <=> CONVERT_TO_LVALUE<C>(u2)) is true,
(t <=> u < 0) == bool(t < u) is true,
(t <=> u > 0) == bool(t > u) is true,
(t <=> u <= 0) == bool(t <= u) is true,
(t <=> u >= 0) == bool(t >= u) is true, and
if Cat is convertible to strong_ordering,T and U modeltotally_ordered_with<T, U> ([concept.totallyordered]).